JEE Main & Advanced Physics NLM, Friction, Circular Motion Sample Paper Topic Test - Friction

  • question_answer
    A worker piles up sand onto a circular area of radius R. No sand is to spill onto the surrounding area. The coefficient of friction of sand on sand is \[\mu \]. The greatest volume of the sand that can be stored in the manner is                                                                         

    A) \[\frac{\pi \mu {{R}^{3}}}{3}\]

    B) \[\frac{\pi \mu {{R}^{3}}}{6}\]

    C) \[\frac{\pi {{R}^{3}}}{3\mu }\]                        

    D) None       

    Correct Answer: A

    Solution :

    The weight component of a particle is balanced by static friction \[mg\sin \theta =\mu (mg\cos \theta )\] \[\mu =\tan \theta =\frac{h}{R}\]
    So \[h=\mu R\]
    Volume \[=\frac{1}{3}\pi {{R}^{2}}h=\frac{1}{3}\pi {{R}^{2}}(\mu R)=\frac{\pi \mu {{R}^{3}}}{3}\]

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